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The first order reliability method requires optimization algorithms to find the minimum distance from the origin to the limit state surface in the normal space. The purpose of this paper is to develop an improved version of the new metaheuristic algorithm inspired from echolocation behaviour of bats, namely, the bat algorithm (BA) dedicated to perform structural reliability analysis.

Modifications have been embedded to the standard BA to enhance its efficiency, robustness and reliability. In addition, a new adaptive penalty equation dedicated to solve the problem of the determination of the reliability index and a proposition on the limit state formulation are presented.

The comparisons between the improved bat algorithm (iBA) presented in this paper and other standard algorithms on benchmark functions show that the iBA is highly efficient, and the application to structural reliability problems such as the reliability analysis of overhead crane girder proves that results obtained with iBA are highly reliable.

A new iBA and an adaptive penalty equation for handling equality constraint are developed to determine the reliability index. In addition, the low computing time and the ease implementation of this method present great advantages from the engineering viewpoint.

The purpose of this paper is to propose variants of an adaptive penalty scheme for steady-state genetic algorithms applied to constrained engineering optimization problems.

For each constraint a penalty parameter is adaptively computed along the evolution according to information extracted from the current population such as the existence of feasible individuals and the level of violation of each constraint. The adaptive penalty method (APM), as originally proposed, computes the constraint violations of the initial population, and updates the penalty coefficient of each constraint after a given number of new individuals are inserted in the population. A second variant, called sporadic APM with constraint violation accumulation, works by accumulating the constraint violations during a given insertion of new offspring into the population, updating the penalty coefficients, and fixing the penalty coefficients for the next generations. The APM with monotonic penalty coefficients is the third variation, where the penalty coefficients are calculated as in the original method, but no penalty coefficient is allowed to have its value reduced along the evolutionary process. Finally, the penalty coefficients are defined by using a weighted average between the current value of a coefficient and the new value predicted by the method. This variant is called the APM with damping.

The paper checks new variants of an APM for evolutionary algorithms; variants of an APM, for a steady-state genetic algorithm based on an APM for a generational genetic algorithm, largely used in the literature previously proposed by two co-authors of this manuscript; good performance of the proposed APM in comparison with other techniques found in the literature; innovative and general strategies to handle constraints in the field of evolutionary computation.

The proposed algorithm has no limitations and can be applied in a large number of evolutionary algorithms used to solve constrained optimization problems.

The proposed algorithm can be used to solve real world problems in engineering as can be viewed in the references, presented in this manuscript, that use the original (APM) strategy. The performance of these variants is examined using benchmark problems of mechanical and structural engineering frequently discussed in the literature.

It is the first extended analysis of the variants of the APM submitted for possible publication in the literature, applied to real world engineering optimization problems.

The purpose of this paper is to present the application of an adaptive bacterial foraging (BF) algorithm for the design optimization of an energy efficient induction motor.

The induction motor design problem is formulated as a mixed integer nonlinear optimization problem. A set of nine independent variables is selected, and to make the machine feasible and practically acceptable, six constraints are imposed on the design. Two different objective functions are considered, namely, the annual active material cost, and the sum of the annual active material cost, annual cost of the active power loss of the motor and annual energy cost required to supply such power loss. A new adaptive BF algorithm is used for solving the optimization problem. A generic penalty function method, which does not require any penalty coefficient, is employed for constraint handling.

The adaptive BF algorithm is validated for two sample motors and benchmarked with the genetic algorithm, particle swarm optimization, simple BF algorithm, and conventional design methods. The results show that the proposed algorithm outperforms the other methods in both the solution quality and convergence rate. The annual cost of the induction motor is remarkably reduced when designed on the basis of minimizing its annual total cost, instead of minimizing its material cost only.

To the best of the knowledge, none of the existing work has applied the BF algorithms for electrical machine design problems. Therefore, the solution to this problem constitutes the main contribution of the paper. According to the huge number of induction motors operating all over the world, the BF techniques used in their design, on minimum annual cost basis, will lead to a tremendous saving in global energy consumption.

Conceiving reliable systems is a strategic issue for any industrial society for its economical and technical development. This paper aims to focus on solving highly constrained redundancy optimization problems in complex systems.

Genetic algorithms (GAs), one of the metaheuristic techniques, have been used and a dynamic adaptive penalty strategy is proposed, which makes use of feedback obtained during the search along with a dynamic distance metric and helps the algorithm to search efficiently for final, optimal or near optimal solution.

The effectiveness of the adaptive penalty function is studied and shown graphically on the solution quality as well as the speed of evolution convergence for several highly constrained problems. The investigations show that this approach can be powerful and robust for problems with large search space, even of size 1017, and difficult‐to‐satisfy constraints.

The results obtained in this paper would be applicable on designing highly reliable systems meeting the requirement of today's society. Moreover, an important advantage of applying GA is that it generates several good solutions (mostly optimal or near optimal) providing a lot of flexibility to decision makers. As such, the paper would be of interest and importance to the system designers, reliability practitioners, as well as to the researchers in academia, business and industry. The paper would have wide applications in the fields of electronics design, telecommunications, computer systems, power systems etc.

Genetic algorithms have been recently used in combinatorial optimization approaches to reliable design, mainly for series‐parallel systems. This paper presents a GA for parallel redundancy optimization problem in complex systems.

The purpose of this paper is to present a new method for solving parametric programming problems; a new scheme of constraints fuzzification. In the proposed approach, constraints are learned based on deductive learning.

Adaptive neural‐fuzzy inference system (ANFIS) is used for constraint learning by generating input and output membership functions and suitable fuzzy rules.

The experimental results show the ability of the proposed approach to model the set of constraints and solve parametric programming. Some notes in the proposed method are clustering of similar constraints, constraints generalization and converting crisp set of constraints to a trained system with fuzzy output. Finally, this idea for modeling of constraint in the support vector machine (SVM) classifier is used and shows that this approach can obtain a soft margin in the SVM.

Properties of the new scheme such as global view of constraints, constraints generalization, clustering of similar constraints, creation of real fuzzy constraints, study of constraint strength and increasing the degree of importance to constraints are different aspects of the proposed method.

The purpose of this paper is to improve and to extend the use of original rank‐niche evolution strategy (RNES) algorithm to solve constrained and unconstrained multiobjective optimization problems.

A new mutation step size is developed for evolution strategy. A mixed ranking procedure is used to improve the quality of the fitness function. A self‐adaptive sharing radius is developed to save computational time. Four constraint‐treating methods are developed to solve constrained optimization problems. Two of them do not use penalty function approach.

The improved RNES algorithm finds better quality Pareto‐optimal solutions more efficiently than the previous version. For most test problems, the solutions obtained by improved RNES are better than, or at least can be compared with, results from other papers.

The application of any evolutionary algorithm to real structural optimization problems would face a problem of spending huge computational time. Some approximate analysis method needs to be incorporated with RNES to solve practical problems.

This paper provides an easier approach to find Pareto‐optimal solutions using an evolutionary algorithm. The algorithm can be used to solve both unconstrained and constrained problems.

The purpose of this paper is to demonstrate the applicability of swarm and evolutionary techniques for regularized machine learning. Generally, by defining a proper penalty function, regularization laws are embedded into the structure of common least square solutions to increase the numerical stability, sparsity, accuracy and robustness of regression weights. Several regularization techniques have been proposed so far which have their own advantages and disadvantages. Several efforts have been made to find fast and accurate deterministic solvers to handle those regularization techniques. However, the proposed numerical and deterministic approaches need certain knowledge of mathematical programming, and also do not guarantee the global optimality of the obtained solution. In this research, the authors propose the use of constraint swarm and evolutionary techniques to cope with demanding requirements of regularized extreme learning machine (ELM).

To implement the required tools for comparative numerical study, three steps are taken. The considered algorithms contain both classical and swarm and evolutionary approaches. For the classical regularization techniques, Lasso regularization, Tikhonov regularization, cascade Lasso-Tikhonov regularization, and elastic net are considered. For swarm and evolutionary-based regularization, an efficient constraint handling technique known as self-adaptive penalty function constraint handling is considered, and its algorithmic structure is modified so that it can efficiently perform the regularized learning. Several well-known metaheuristics are considered to check the generalization capability of the proposed scheme. To test the efficacy of the proposed constraint evolutionary-based regularization technique, a wide range of regression problems are used. Besides, the proposed framework is applied to a real-life identification problem, i.e. identifying the dominant factors affecting the hydrocarbon emissions of an automotive engine, for further assurance on the performance of the proposed scheme.

Through extensive numerical study, it is observed that the proposed scheme can be easily used for regularized machine learning. It is indicated that by defining a proper objective function and considering an appropriate penalty function, near global optimum values of regressors can be easily obtained. The results attest the high potentials of swarm and evolutionary techniques for fast, accurate and robust regularized machine learning.

The originality of the research paper lies behind the use of a novel constraint metaheuristic computing scheme which can be used for effective regularized optimally pruned extreme learning machine (OP-ELM). The self-adaption of the proposed method alleviates the user from the knowledge of the underlying system, and also increases the degree of the automation of OP-ELM. Besides, by using different types of metaheuristics, it is demonstrated that the proposed methodology is a general flexible scheme, and can be combined with different types of swarm and evolutionary-based optimization techniques to form a regularized machine learning approach.

The purpose of this paper is to propose a new scheme for obtaining acceptable solutions for problems of continuum topology optimization of structures, regarding the distribution and limitation of discretization errors by considering h-adaptivity.

The new scheme encompasses, simultaneously, the solution of the optimization problem considering a solid isotropic microstructure with penalization (SIMP) and the application of the h-adaptive finite element method. An analysis of discretization errors is carried out using an a posteriori error estimator based on both the recovery and the abrupt variation of material properties. The estimate of new element sizes is computed by a new h-adaptive technique named “Isotropic Error Density Recovery”, which is based on the construction of the strain energy error density function together with the analytical solution of an optimization problem at the element level.

Two-dimensional numerical examples, regarding minimization of the structure compliance and constraint over the material volume, demonstrate the capacity of the methodology in controlling and equidistributing discretization errors, as well as obtaining a great definition of the void–material interface, thanks to the h-adaptivity, when compared with results obtained by other methods based on microstructure.

This paper presents a new technique to design a mesh made with isotropic triangular finite elements. Furthermore, this technique is applied to continuum topology optimization problems using a new iterative scheme to obtain solutions with controlled discretization errors, measured in terms of the energy norm, and a great resolution of the material boundary. Regarding the computational cost in terms of degrees of freedom, the present scheme provides approximations with considerable less error if compared to the optimization process on fixed meshes.

The purpose of this paper is devoted to present an accurate assessment for determine natural frequencies for uniform and non-uniform Euler-Bernoulli beams and frames by an adaptive generalized finite element method (GFEM). The present paper concentrates on developing the C1 element of the adaptive GFEM for vibration analysis of Euler-Bernoulli beams and frames.

The variational problem of free vibration is formulated and the main aspects of the adaptive GFEM are presented and discussed. The efficiency and convergence of the proposed method in vibration analysis of uniform and non-uniform Euler-Bernoulli beams are checked. The application of this technique in a frame is also presented.

The present paper concentrates on developing the C1 element of the adaptive GFEM for vibration analysis of Euler-Bernoulli beams and frames. The GFEM, which was conceived on the basis of the partition of unity method, allows the inclusion of enrichment functions that contain a priori knowledge about the fundamental solution of the governing differential equation. The proposed enrichment functions are dependent on the geometric and mechanical properties of the element. This approach converges very fast and is able to approximate the frequency related to any vibration mode.

The main contribution of the present study consisted in proposing an adaptive GFEM for vibration analysis of Euler-Bernoulli uniform and non-uniform beams and frames. The GFEM results were compared with those obtained by the h and p-versions of FEM and the c-version of the CEM. The adaptive GFEM has shown to be efficient in the vibration analysis of beams and has indicated that it can be applied even for a coarse discretization scheme in complex practical problems.

The purpose of this paper is to develop a mathematical model for the design of robust layout for unequal area-dynamic facility layout problem with flexible bay structure (UA-DFLP with FBS) and test the suitability of generated robust layout in a dynamic environment.

This research adopts formulation of a mathematical model for generating a single layout for unequal area facility layout problems with flexible bay structure under dynamic environment. The formulated model for the robust layout formation is solved by developing a simulated annealing algorithm. The proposed robust approach model for UA-DFLP with FBS is validated by conducting numerical experiments on standard UA-DFLPs reported in the literature. The suitability of the generated robust layout in a dynamic environment is tested with total penalty cost criteria.

The proposed model has given a better solution for some UA-DFLPs with FBS in comparison with the adaptive approach’s solution reported in the literature. The total penalty cost is within the specified limit given in the literature, for most of the layouts generated for UA-DFLPs with FBS. In the proposed model, there is no rearrangement of facilities in various periods of planning horizon and thus no disruptions in operations.

The present work has limitations that when the area and aspect ratio of the facilities are required to change from one period to another, then it is not possible to make application of the robust approach-based formulation to the dynamic environment facility layout problems.

Rearrangement of facilities in adaptive approach disrupts the operations whereas in the proposed approach no disruption of production. The FBS approach is more suitable for layout planning where proper aisle structure is required. The solution of the proposed approach helps to create a proper aisle structure in the detailed layout plan. Thus, easy interaction of the material handling equipment, men and materials is possible.

This paper proposes a mathematical formulation for the design of robust layout for UA-FLPs with FBS in a dynamic environment and an efficient simulated annealing algorithm as its solution procedure. The proposed robust approach generates a single layout for the entire planning horizon. This approach is more useful for facilities which are difficult/sensitive to relocate in various periods of the planning horizon.